SRC/zgglse.f(3)

NAME
SRC/zgglse.f

SYNOPSIS

  Functions/Subroutines
subroutine zgglse (m, n, p, a, lda, b, ldb, c, d, x, work, lwork, info)
ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Function/Subroutine Documentation

  subroutine zgglse (integer m, integer n, integer p, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( * ) c, complex*16, dimension( * ) d, complex*16, dimension( * ) x, complex*16, dimension( * ) work, integer lwork, integer info)

ZGGLSE solves overdetermined or underdetermined systems for OTHER matrices

Purpose:

    !>
    !> ZGGLSE solves the linear equality-constrained least squares (LSE)
    !> problem:
    !>
    !>         minimize || c - A*x ||_2   subject to   B*x = d
    !>
    !> where A is an M-by-N matrix, B is a P-by-N matrix, c is a given
    !> M-vector, and d is a given P-vector. It is assumed that
    !> P <= N <= M+P, and
    !>
    !>          rank(B) = P and  rank( (A) ) = N.
    !>                               ( (B) )
    !>
    !> These conditions ensure that the LSE problem has a unique solution,
    !> which is obtained using a generalized RQ factorization of the
    !> matrices (B, A) given by
    !>
    !>    B = (0 R)*Q,   A = Z*T*Q.
    !>
    !> Callers of this subroutine should note that the singularity/rank-deficiency checks
    !> implemented in this subroutine are rudimentary. The ZTRTRS subroutine called by this
    !> subroutine only signals a failure due to singularity if the problem is exactly singular.
    !>
    !> It is conceivable for one (or more) of the factors involved in the generalized RQ
    !> factorization of the pair (B, A) to be subnormally close to singularity without this
    !> subroutine signalling an error. The solutions computed for such almost-rank-deficient
    !> problems may be less accurate due to a loss of numerical precision.
    !>
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrices A and B. N >= 0.
    !>

    P

    !>          P is INTEGER
    !>          The number of rows of the matrix B. 0 <= P <= N <= M+P.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the elements on and above the diagonal of the array
    !>          contain the min(M,N)-by-N upper trapezoidal matrix T.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,M).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,N)
    !>          On entry, the P-by-N matrix B.
    !>          On exit, the upper triangle of the subarray B(1:P,N-P+1:N)
    !>          contains the P-by-P upper triangular matrix R.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B. LDB >= max(1,P).
    !>

    C

    !>          C is COMPLEX*16 array, dimension (M)
    !>          On entry, C contains the right hand side vector for the
    !>          least squares part of the LSE problem.
    !>          On exit, the residual sum of squares for the solution
    !>          is given by the sum of squares of elements N-P+1 to M of
    !>          vector C.
    !>

    D

    !>          D is COMPLEX*16 array, dimension (P)
    !>          On entry, D contains the right hand side vector for the
    !>          constrained equation.
    !>          On exit, D is destroyed.
    !>

    X

    !>          X is COMPLEX*16 array, dimension (N)
    !>          On exit, X is the solution of the LSE problem.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK. LWORK >= max(1,M+N+P).
    !>          For optimum performance LWORK >= P+min(M,N)+max(M,N)*NB,
    !>          where NB is an upper bound for the optimal blocksizes for
    !>          ZGEQRF, CGERQF, ZUNMQR and CUNMRQ.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          = 1:  the upper triangular factor R associated with B in the
    !>                generalized RQ factorization of the pair (B, A) is exactly
    !>                singular, so that rank(B) < P; the least squares
    !>                solution could not be computed.
    !>          = 2:  the (N-P) by (N-P) part of the upper trapezoidal factor
    !>                T associated with A in the generalized RQ factorization
    !>                of the pair (B, A) is exactly singular, so that
    !>                rank( (A) ) < N; the least squares solution could not
    !>                    ( (B) )
    !>                be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 188 of file zgglse.f.

Author

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